Problem: Solve for $x$ and $y$ using substitution. ${-5x+5y = 5}$ ${x = 3y+7}$
Answer: Since $x$ has already been solved for, substitute $3y+7$ for $x$ in the first equation. ${-5}{(3y+7)}{+ 5y = 5}$ Simplify and solve for $y$ $-15y-35 + 5y = 5$ $-10y-35 = 5$ $-10y-35{+35} = 5{+35}$ $-10y = 40$ $\dfrac{-10y}{{-10}} = \dfrac{40}{{-10}}$ ${y = -4}$ Now that you know ${y = -4}$ , plug it back into $\thinspace {x = 3y+7}\thinspace$ to find $x$ ${x = 3}{(-4)}{ + 7}$ $x = -12 + 7$ ${x = -5}$ You can also plug ${y = -4}$ into $\thinspace {-5x+5y = 5}\thinspace$ and get the same answer for $x$ : ${-5x + 5}{(-4)}{= 5}$ ${x = -5}$